The strict assumption that information flows along shortest paths (geodesics) is not
always appropriate, as discussed, for example, by Newman [1]}, who proposes a random walk betweenness measure computed using matrix methods.
An important criticism of the geodesic viewpoint, which also motivates the random walk alternative, is that when passing messages to target nodes, typical
users do not have the global network information and hence may not be aware of
the shortest paths between pairs of nodes to be able to place them along the correct route.
The runtime for this random walk betweenness measure is \(\Omega \left(\left(M+N\right)N^2 \right)\)  and the algorithm requires matrix inversions.
We also note that these two betweenness measures above are designed for static
networks, and changes in the size of communities over time
can affect the distribution of the betweenness values amongst the nodes.
